Multiplication and Division

Multiplication and Division

Aims for this evening

Talk you through the main ways in which we teach X and See the children in action2.Tips for helping your child at home3.Some useful resources and wbebsites

Main sources of advice and guidanceAs I showed last time, these are three of the main sources of information and guidance that we use. Explain3

Key things to remember

1. The importance of developing rapid recall of number facts such as times tables, doubling and halving and quick working out of fractions is vital

2. The development of mental strategies begins before written methods and then runs parallel to them it is the thing that children will use most in life

3. Formal methods are important but not at the expense of understanding (efficient methods are used increasingly as the children get older)

4. The language of and discussion in maths is important i.e. an important term for the children to know with multiplication is product as this is used a lot3. E.g. if you teach a formal efficient method too early it becomes purely about memory whereas if the children have parctical, mental based 4

MultiplicationInformal groups > numberline > arraysWhen children experience multiplication in the early part of school they will look at the idea of repeated addition. They use practical apparatus, drawn or real hoops to put objects in. They will then use their ability to count in steps of 2 or 3 for example to get to their number. At this point the examples will be very practical based such as Mrs. Newton is going to give Bob, Bill, Sarah and Jane 3 sweets each. How many sweets will she need to have?

As this becomes second nature to the children (end of year 1 beginning of Year 2) the teacher might begin to use a number line to support counting in equal steps. By doing this it begins to open the children to the idea that multiplication is commutative i.e. it can be done in either direction. This would be supported by the work that the teacher is doing on times tables such as 2X3 = 6 and 3X2 = 6

From there (commonly used in Y2) children may be shown multiplication as an array. Using dots or apparatus children can begin to see much more clearly that 5 x 3 is five lots of three and also 3 lots of five. They also begin to see that 15 divided by 3 equals 5 and 15 divided by 5 equals 3.5Multiplication

Grid method (efficient) > formal (efficient)

By this stage we are into Y3 onwards and the strategies become more efficient. They will start with the grid method on the left where they are expected to do a 2digit number times a 1 digit number. It is worth saying here that it is still important for the children to use their mental strategies as it is not always the case that children will need to use a written method just because the numbers are larger. As an example 17 X 3 might initially seem quite tricky to a Y3 child but in actual fact, that vast majority of them could do 10 X 3 and then 7X3 and add them together to make 51.

Grid method is then used as the main strategy until the children are ready to move onto formal strategies which, for many might not be until the very end of Y6. The important thing is not to confuse the children with a news strategy before they are really secure in a different one (unless they are not getting the first one!)

Once they are ready then they will do formal6

There are 4 apples in each pack.

Mrs Pullen buys 3 packs of apples.How many apples does she buy?Work out the number that is halfway between 27 38 and 33 38Show your working.

(this one might be easier than it looks)Multiplication examples from Y1/2 and from Y6

Division

Dividend the big numberDivisor the small number

As with multiplication, division starts off with informal methods and then as the children become more able to apply mental strategies and as the numbers and contexts become more difficult they move towards efficient methods.

Division is split into sharing and grouping. There are differences between which type of questions are sharing and grouping but essentially once the numbers become too large for easy use of actually sharing things then it is grouping.

The main difference about the way we have to think about sharing and grouping is that, in the main sharing starts with the larger number and subtracts multiples of the divisor until there is as close to nothing left and grouping is that you start with the divisor and work out how many lots of that number you can fit into the larger number.

The children will use simple sharing practices and grouping objects considering everyday examples in KS1 and especially in Y1. As the children move through Y1 they will continue with practical aspects but begin to relate it more to their understanding of times tables and also begin to understand remainders that they express as numbers.

Once they get onto larger numbers they will use a number line to plot their progress of groups so in the example here 96 divided by 6 the pupils would be expected to know that 6 goes into 60 ten times and then they are left with 36 and 6 goes into 36 six times. The number line helps the children keep track of where they are.

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Note about remainders: remainders as numbers in KS1 and Y3. Increasingly expressed as fractions as children move into Y5,6. E.g. 36 5 = 6r1 in Y3 but 6 and 1/5 in Y5The next step on from that is to start to plot it in a formal bus stop format.To begin with you can see that the children have still used their partitioning skills to break the calculation into a more manageable chunk. This has the added benefit of showing the children what they are actually doing when they do the bus stop method.

Following this they move into a formal bus stop algorithm that you would have used when you were at school. In Kemble this replaces the until recently taught chunking method of division. We looked carefully at what the children were getting wrong and talked to the children about why and it became clear that they did not understand chunking. This was backed up by what is written in the Ofsted research.

A slight difference come when doing two digit numbers. Again, we found that in the trials we did children actually got more questions right when they did a normal and not long division calculation and had some jottings on the side to help them if they needed it.9What nextGo and see your childs teacherHave a look at some websites Hang around here and ask any questions

Have a look at the school website

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